How Do You Apply Trigonometric Substitution to Integrate Sqrt(X^2 + 9)?

In summary, the conversation is about evaluating the integral of Sqrt[(x^2)+9] using the Trigonometric substitution technique. The person is asking for help and mentioning that they are new to this concept and their textbook is not helpful. They also share their attempt at a solution by setting x=3sin(u) and dx=3cos(u). They mention a website that explains the technique and conclude by saying they are not sure if their solution is correct.
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cooltee13
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Homework Statement


Evaluate the Integral: Sqrt[(X^2)+9]

Homework Equations


I know its an Integration By parts problem, but I don't know how to start it.


The Attempt at a Solution



Im JUST learning this as I type this problem out, I've just been stuck on it for a while and my book does a horrible job of explaining how to do problems. If anybody could explain the Trigonometric substitution technique or knows of a good website that explains it I would be very grateful.

For this problem though, all I did was set x=3sin(u) and dx=3cos(u).

I don't know if that's right though, because like I said, I just "learned" this yesterday
 
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FAQ: How Do You Apply Trigonometric Substitution to Integrate Sqrt(X^2 + 9)?

What is Trigonometric Substitution?

Trigonometric substitution is a method used to evaluate integrals involving expressions that contain radicals or algebraic terms. It involves substituting trigonometric functions for these expressions in order to simplify the integral and make it easier to solve.

When is Trigonometric Substitution used?

Trigonometric substitution is used when integrals involve expressions such as √(a^2 - x^2), √(x^2 - a^2), or √(x^2 + a^2). These expressions can be simplified using trigonometric substitutions and the resulting integral can be solved using trigonometric identities.

What are the three types of Trigonometric Substitution?

The three types of Trigonometric Substitution are:
1. Substitution for √(a^2 - x^2): In this type, the expression √(a^2 - x^2) is substituted with a sinθ or a cosθ.
2. Substitution for √(x^2 + a^2): In this type, the expression √(x^2 + a^2) is substituted with x tanθ or x secθ.
3. Substitution for √(x^2 - a^2): In this type, the expression √(x^2 - a^2) is substituted with x secθ or x tanθ.

What are the steps to use Trigonometric Substitution?

The steps to use Trigonometric Substitution are:
1. Identify the type of substitution needed based on the expression in the integral.
2. Substitute the appropriate trigonometric function for the expression.
3. Use trigonometric identities to simplify the resulting integral.
4. Solve the simplified integral.
5. Substitute back the original variable and simplify the final answer.

What are some common mistakes to avoid when using Trigonometric Substitution?

Some common mistakes to avoid when using Trigonometric Substitution are:
1. Forgetting to change the limits of integration when substituting for a new variable.
2. Using the wrong trigonometric identity or making a mistake when simplifying the integral.
3. Forgetting to substitute back the original variable in the final answer.
4. Using Trigonometric Substitution when another integration method would be more efficient.
5. Not being familiar with basic trigonometric identities, which can lead to errors when simplifying the integral.

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